An HTML file cannot include a php file in the sense you're asking, because a .php file is being processed by the server and is (generally) outputting HTML.
Your example...
I can import php like this:
<form action="file.php">
is not "importing" php, it is directing the form POST to a php file to be processed, which then outputs HTML as its response.
In general, when doing PHP programming, you are writing .php files instead of writing .html files. If something needs to use PHP code it should be in a .php file, not a .html file which normally has completely static content.
There is a way to have your PHP processor act upon .html files, and that is to configure Apache (or whatever your webserver is) to hand .html files to PHP in the same way it is configured to handle .php files — but then you are incurring the overhead of processing every .html file whether or not it actually has PHP code in it.